Qualitative comparisons of experimental results on deterministic freak wave generation based on modulational instability

Abstract

A number of qualitative comparisons of experimental results on unidirectional freak wave generation in a hydrodynamic laboratory are presented in this paper. A nonlinear dispersive type of wave equation, the nonlinear Schr\"{o}dinger equation, is chosen as the theoretical model. A family of exact solutions of this equation the so-called Soliton on Finite Background describing modulational instability phenomenon is implemented in the experiments. It is observed that all experimental results show an amplitude increase according to the phenomenon. Both the carrier wave frequency and the modulation period are preserved during the wave propagation. As predicted by the theoretical model, a phase singularity is also observed in the experiments. Due to frequency downshift phenomenon, the experimental signal and spectrum lose their symmetric property. Another qualitative comparison indicates that the Wessel curves for the experimental results are the perturbed version of the theoretical ones.